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  • Need solution for RD Sharma Maths Class 12 Chapter 29 Linear Programmig Excercise 29.4 Question 18

Need solution for RD Sharma Maths Class 12 Chapter 29 Linear Programmig Excercise 29.4 Question 18

Answers (1)

Answer:

Max Profit = Rs.16 when 8 souvenirs of Type A and 20 Souvenirs of Type B is produced.

Hint:

Form Linear Equation and solve graphically.

Given:

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 min each for cutting and 10 min each for assembling. Souvenirs of type B require 8 min each for cutting and 8 min each for assembling. There are 3 hours 20 min available for cutting and 4 hours available for assembling. The profit is 50 paise each of type A and 60 paise each of type B souvenirs.

Solution:

Let the company manufacture x souvenirs of Type A and y souvenirs of Type B

Therefore,

x\geq 0,y\geq 0

The given information can be compiled in a table as follows:

 

Type A

Type B

Availability

Cutting(min)

5

8

3×60+20=200

Assembling (min)

10

8

4×60=240

 

The profit on type A souvenirs is 50 paise and on Type B souvenirs is 60 paise. Therefore, profit gained on x souvenirs of type A and y souvenirs of type B is Rs.0.50 x and Rs. 0.60 y respectively

Total Profit, z= 50x+60y
The mathematical formulation of the given problem is,

max: z= 50x+60y , Subject x constraint,

\begin{aligned} &5 x+8 y \leq 200 \\ &10 x+8 y \leq 240 \\ &x \geq 0, y \geq 0 \end{aligned}

 

Region  5x+8y \leq 200  : The line  5x+8y=200  meets the axes at A(40,0) , B(0,25) respectively.

 

Region containing origin represents the solution of the in equation 5x+8y \leq 200  as (0,0) satisfy satisfies 5x+8y \leq 200

Region 10x+8y\leq 240  : line 10x+8y=240  meets axes at C(24,0),D(0,30) respectively.
Region containing origin represents the solution of in equation  10x+8y\leq 240   as (0,0) satisfies 10x+8y\leq 240
Region  x,y\geq 0  : it represents first quadrant.

The corner points are  O(0,0),B(0,25),\epsilon (8,20),C(24,0)

The value of z at these corner points are as follows.

Corner Points

z=50x+60y

O

0

B

1500

\epsilon

1600

C

1200

Thus, 8 souvenirs of Type A and 20 souvenirs of Type B should be produced each day to get the maximum profit of Rs16

Posted by

infoexpert27

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